Figure 6 - uploaded by Jason F. Shepherd
Content may be subject to copyright.
25. Hexahedral mesh of the part29 model. Images of the mesh from the front, back and bottom are shown, respectively.
Similar publications
This paper presents a fast an robust mesh generation procedure that is able to generate meshes of the earth system (ocean and continent) in matters of seconds. Our algorithm takes as input a standard shape-file i.e. geospatial vector data format for geographic information system (GIS) software. The input is initially coarsened in order to automatic...
This paper presents an algorithm for automatic unstructured mesh generation that works with cutouts of parametric surfaces with arbitrary domains and big curvatures. Parametric surfaces are generally quadrilateral and triangular areas, but many applications use complex areas, resulting from the original domain cutouts at intersections function or u...
Fictitious domain methods such as the finite cell method simplify the discretization process significantly as the mesh is decoupled from the geometrical description. However, this simplification in the mesh generation results in broken cells, which is why special integration methods are required. Usually, adaptive integration schemes are applied re...
Based upon a momentum-source method, a numerical simulation method has been developed to calculate the tip-jet drive rotor/fuselage flowfield. The momentum-source term is used to describe the effect of rotor on its flowfield. The mass-source term is used to describe the tip-jet. According to the characteristics of rotor/fuselage flowfield and requi...
Citations
... Finite Elements must be convex and inversion free to be usable in this context. This property can be proved by showing that the Scaled Jacobian of all elements is positive [15]. Besides this requirement a wide range of mesh quality metrics exist. ...
This paper describes a novel method of generating hex-dominant meshes using pre-computed optimal subdivisions of the unit cube in a grid-based approach. Our method addresses geometries that are standard in mechanical engineering and often must comply with the restrictions of subtractive manufacturability. A central component of our method is the set of subdivisions we pre-compute with Answer Set Programming. Despite being computationally expensive, we obtain optimal meshes of up to 35 nodes available to our method in a template fashion. The first step in our grid-based method generates a coarse Precursor Mesh for meshing complete parts representing the bar stock. Then, the resulting mesh is generated in a subtractive manner by inserting and fitting the pre-generated subdivisions into the Precursor Mesh. This step guarantees that the elements are of good quality. In the final stage, the mesh nodes are mapped to geometric entities of the target geometry to get an exact match. We demonstrate our method with multiple examples showing the strength of this approach.
... Finite Elements must be convex and inversion free to be usable in this context. This property can be proved by showing that the Scaled Jacobian of all elements is positive [15]. Besides this requirement a wide range of mesh quality metrics exist. ...
This paper describes a novel method of generating hex-dominant meshes using pre-computed optimal subdivisions of the unit cube in a grid-based approach. Our method addresses geometries that are standard in mechanical engineering and often must comply with the restrictions of subtractive manufacturability. A central component of our method is the set of subdivisions we pre-compute with Answer Set Programming. Despite being computationally expensive, we obtain optimal meshes of up to 35 nodes available to our method in a template fashion. The first step in our grid-based method generates a coarse Precursor Mesh for meshing complete parts representing the bar stock. Then, the resulting mesh is generated in a subtractive manner by inserting and fitting the pre-generated subdivisions into the Precursor Mesh. This step guarantees that the elements are of good quality. In the final stage, the mesh nodes are mapped to geometric entities of the target geometry to get an exact match. We demonstrate our method with multiple examples showing the strength of this approach.
... Hex mesh has been widely studied for decades. However, an automatic method that can generate high quality hex-meshes for any complex geometry is still unavailable because of the strong topological constraints [11], i.e., the dual chord and the dual sheet. Some methods were devised for specific types of geometries. ...
In this paper, we propose an improved singularity structure simplification method for hexahedral (hex) meshes using a weighted ranking approach. In previous work, the selection of to-be-collapsed base complex sheets/chords is only based on their thickness, which will introduce a few closed-loops and cause an early termination of simplification and a slow convergence rate. In this paper, a new weighted ranking function is proposed by combining the valence prediction function of local singularity structure, shape quality metric of elements and the width of base complex sheets/chords together. Adaptive refinement and local optimization are also introduced to improve the uniformity and aspect ratio of mesh elements. Compared to thickness ranking methods, our weighted ranking approach can yield a simpler singularity structure with fewer base-complex components, while achieving comparable Hausdorff distance ratio and better mesh quality. Comparisons on a hex-mesh dataset are performed to demonstrate the effectiveness of the proposed method.
... However, it has been shown that a 3-octree [182,119], defined as a data structure where a cell is divided into 27 new cells [220] is more suitable for hexahedral mesh generation. Reviews about the subject can be found in [247,227]. ...
The stronger competition with other means of transportation has increased the demand for performance in the railway industry. One way to achieve higher performance is using accurate numerical models to design/predict railways tracks behaviour. Two classes of numerical models are commonly used to predict the behaviour of these systems: (i) discrete approaches and (ii) continuum approaches. In the former, each grain of the ballast is represented by a rigid body and interacts with its neighbours through nonlinear contact forces using, for example, the nonsmooth contact dynamics method. Due to computational limits, this kind of method can only solve a few meters-length of ballast. The coupling with the soil under the ballast layer and with the sleepers also remains an open problem. In continuum approaches, the ballast is replaced by a homogenized continuum and the classical Finite Element (FE) Method (or similar) is used. However, they are normally used with homogeneous mechanical parameters, so that they do not represent fully the heterogeneity of the strains and stresses within the ballast layer. We investigate in this thesis an alternative approach using a stochastic heterogeneous continuum model, that can be solved with a FElike method while retaining to a large degree the heterogeneity of the stress and strain fields. The objective of this continuous model is to represent statistically the heterogeneity of the stress field in a continuum model as well as in a discrete granular model. To do this, the mechanical properties are represented using random fields. The present thesis is divided into three parts: (1) the construction of the model and the identification of the parameters of the continuum material (first-order marginal density, mean, variance, correlation model, and correlation length); (2) wave propagation in a ballasted railway track. (3) preliminary exploration of two experimental datasets. The first part sets the randomly-fluctuating continuum model and identifies the parameters of our continuum model on small cylindrical samples of discrete ballast. Continuum models equivalent to the discrete samples are generated and solved using the FE method, and the stochastic field used as mechanical properties. An optimization process is used to find a normalized variance for the stochastic heterogeneous material. The second part of this work concentrates on the solution of the dynamical equations on a large-scale model of a ballasted railway track using the Spectral Element Method. The influence of the heterogeneity is highlighted and studied. As a result, dispersion curves are obtained. Finally, the third part presents two distinct datasets of experimental measurements on ballast material: (1) a ballast box; (2) a train passage in a segment of ballasted railway track. Mobility curves were extracted from the ballast box experiment. An inverse problem was solved in order to estimate the homogenized wave velocity and local wave velocity in the medium. The trains pass-by recorded for the analysis of the vibration at medium frequencies.
... For this reason, polycube-based hex-meshes often require a post-processing step referred to as padding (or pillowing [MT95]) on the entire domain boundary. As detailed by Shepherd [She07,SJ08], the padding operation starts with an initial mesh from which a subset of hexahedra is defined to create a shrink set. The shrink set is separated from the original mesh and shrunk. ...
Hexahedral meshes generated from polycube mapping often exhibit a low number of singularities but also poor‐quality elements located near the surface. It is thus necessary to improve the overall mesh quality, in terms of the minimum scaled Jacobian (MSJ) or average SJ (ASJ). Improving the quality may be obtained via global padding (or pillowing), which pushes the singularities inside by adding an extra layer of hexahedra on the entire domain boundary. Such a global padding operation suffers from a large increase of complexity, with unnecessary hexahedra added. In addition, the quality of elements near the boundary may decrease. We propose a novel optimization method which inserts sheets of hexahedra so as to perform selective padding, where it is most needed for improving the mesh quality. A sheet can pad part of the domain boundary, traverse the domain and form singularities. Our global formulation, based on solving a binary problem, enables us to control the balance between quality improvement, increase of complexity and number of singularities. We show in a series of experiments that our approach increases the MSJ value and preserves (or even improves) the ASJ, while adding fewer hexahedra than global padding.
... Hex mesh has been widely studied for decades. However, an automatic method that can generate high quality hex-meshes for any complex geometry is still unavailable because of the strong topological constraints [8], i.e., the dual chord and the dual sheet. Unlike tetrahedral meshes, any local changes in the mesh would propagate to the whole mesh by dual chords or dual sheets [8], which makes hex-mesh generation a very challenging task. ...
... However, an automatic method that can generate high quality hex-meshes for any complex geometry is still unavailable because of the strong topological constraints [8], i.e., the dual chord and the dual sheet. Unlike tetrahedral meshes, any local changes in the mesh would propagate to the whole mesh by dual chords or dual sheets [8], which makes hex-mesh generation a very challenging task. Some methods were devised for specific types of geometries. ...
In this paper, we propose an improved singularity structure simplification method for hexahedral (hex) meshes using a weighted ranking approach. In previous work, the selection of to-be-collapsed base complex sheets/chords is only based on their thickness, which will introduce a few closed-loops and cause an early termination of simplification and a slow convergence rate. In this paper, a new weighted ranking function is proposed by combining the valence prediction function of local singularity structure, shape quality metric of elements and the width of base complex sheets/chords together. Adaptive refinement and local optimization are also introduced to improve the uniformity and aspect ratio of mesh elements. Compared to thickness ranking methods, our weighted ranking approach can yield a simpler singularity structure with fewer base-complex components, while achieving comparable Hausdorff distance ratio and better mesh quality. Comparisons on a hex-mesh dataset are performed to demonstrate the effectiveness of the proposed method.
... Similar to other polycube-based hex-mesh generation techniques [GSZ11, LVS * 13, HJS * 14], we insert a padding layer [She07] to each of the hex-meshes shown in our result section (except the robot hex-mesh). To improve the geometric quality of these hex-meshes, we first improve the regularity of the distribution of their elements using the parametric-domain based optimization [GDC15], and then untangle the flipped hexahedral elements through the edge-cone based optimization [LSVT15], followed by the quality improvement scheme proposed in [BDK * 03]. ...
Hexahedral (or Hex-) meshes are preferred in a number of scientific and engineering simulations and analyses due to their desired numerical properties. Recent state-of-the-art techniques can generate high-quality hex-meshes. However, they typically produce hex-meshes with uniform element sizes and thus may fail to preserve small-scale features on the boundary surface. In this work, we present a new framework that enables users to generate hex-meshes with varying element sizes so that small features will be filled with smaller and denser elements, while the transition from smaller elements to larger ones is smooth, compared to the octree-based approach. This is achieved by first detecting regions of interest (ROIs) of small-scale features. These ROIs are then magnified using the as-rigid-as-possible deformation with either an automatically determined or a user-specified scale factor. A hex-mesh is then generated from the deformed mesh using existing approaches that produce hex-meshes with uniform-sized elements. This initial hex-mesh is then mapped back to the original volume before magnification to adjust the element sizes in those ROIs. We have applied this framework to a variety of man-made and natural models to demonstrate its effectiveness.
... The grid-based method is relatively simple to implement and easy to realize the local refinement. Recently, with the development of the adaptive techniques of mesh generation, grid-based method is modified by many researchers and used widely in the mesh [12][13][14]. Unfortunately, there are no demonstrated methods for creating grid-based, good-quality, reasonably density distributed hexahedral meshes. ...
Purpose: The quality of the finite element mesh is one of the important factors which determine the precision and accuracy of finite element analysis. A density control based adaptive hexahedral mesh generation algorithm for three dimensional models is presented in this paper. Methodology: The main idea of the adaptive grid-based mesh generation algorithm is similar to those of other conventional grid-based methods, but the initial grid structure is generated adaptively based on the geometric features of the solid model. Findings: The density control based hexahedral mesh generation algorithm can accurately capture the geometric features of the solid model with the least number of elements and can generate high quality of hexahedral element meshes. originality: A spatial refinement field is constructed in this paper to control the mesh size and density distribution based on the geometric factors of the solid model. Practical value: Conformal hexahedral element meshes which can capture all the geometry characters of the solid models and meet finite element analysis are generated. The effectiveness of the algorithm and quality of the mesh generation are demonstrated by using a mechanical model.
... In finite element analysis, hexahedral meshes are usually preferred to tetrahedral meshes due to higher accuracy, faster convergence and lighter storage [2,3]. Therefore, many researchers have been committed to the research of hex meshing for decades. ...
Sheet inflation is an enhanced and more general version of the classic pillowing procedure[1] used to modify hexahedrdal meshes. The flexibility of sheet inflation makes it a valuable tool for hex mesh generation, modification and topology optimization. However, it is still difficult to generate self-intersecting sheet within a local region while assuring the mesh quality. This paper proposes an approach to achieving optimized complex sheet inflation under various constraints. The approach can generate complex sheets that intersect themselves more than once and maximize the quality of the resultant mesh. We successfully apply this approach to mesh matching and mesh boundary optimizing.
... Some related concepts are also defined in this section. Due to the limited space of this paper, however, we leave out some more common concepts such as hexahedral mesh, sheet and quadrilateral mesh, which can be found in previous studies [1,8,9,11,12]. We first introduce the shared geometric face of the interfaces, then give the chord's definition and investigate some of its topological properties first and finally propose the chord-matching criteria. ...
... ValVar(e ′ ui ). Fig. 18b In Fig. 18a, e 11 and e 10 are first merged to form e 14 in Fig. 18b, which is then removed during the sheet extraction in Fig. 18c. e 9 is also removed during the sheet extraction ...
Mesh matching is an effective way to convert the non-conforming interfaces between two hexahedral meshes into conforming ones, which is very important for achieving high-quality finite element analysis. However, the existing mesh matching algorithm is neither efficient nor effective enough to handle complex interfaces and self-intersecting sheets. In this paper, the algorithm is improved in three aspects: (1) by introducing a more precise criteria for chord matching and the concept of partition chord set, complex interfaces with internal loops can be handled more effectively; (2) by proposing a new solution, self-intersecting sheet can be inflated and extracted locally; and (3) by putting forward a mesh quality evaluation method, the sheet extraction operation during mesh matching can be done more efficiently. Our improved mesh matching algorithm is fully automatic, and its effectiveness is demonstrated by several examples in different matching situations.
